| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | last | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 207 |
Modelling Fecal Cortisol Metabolites
Dr. Nicolas Ferry - Bavarian National Forest Park / Daniel Schlichting - StabLab
31 Jan 2025
Model FCM levels on spatial and temporal distance to hunting activities.
Expectation: FCM levels higher when closer in time and space.
Contains information of 809 faecal samples, including
Deer location at the time of hunting event is approximated by linear interpolation.
To identify relevant Hunting Events respective to a given FCM Sample, we introduce three selection parameters:
Among the relevant hunting events, the most relevant one is defined by one of the three introduced proximity criteria:
A hunting event is considered relevant to a FCM sample, if
We suggest three different Datasets for Modelling
| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | last | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 207 |
For Modelling, we consider the following covariates, defined for each pair of FCM sample and most relevant hunting event:
| Model | Type | Non-Parametric Effects | Linear Effects | Random Intercept | Distribution Assumption |
|---|---|---|---|---|---|
| A | GAMM | Time Difference, Distance, Sample Delay, Day of Year | Pregnant, Number Other Hunts | None | Gamma |
| B | XGBoost | Uses all covariates as input features, learning interactions through decision trees | None | None | No specific distribution assumption |
Log link for interpretability.
Let \(i = 1,\dots,N\) be the indices of deer and \(j = 1,\dots,n_i\) be the indices of FCM measurements for each deer.
\[ \begin{eqnarray} \textup{FCM}_{ij} &\sim& \mathcal{Ga}\left( \nu, \frac{\nu}{\mu_{ij}} \right) \\ \mu_{ij} &=& \mathbb{E}(\textup{FCM}_{ij}) = \exp(\eta_{ij}) \\ \eta_{ij} &=& \beta_0 + \beta_1 \textup{Pregnant}_{ij} + \beta_2 \textup{NumberOtherHunts}_{ij} + \\ && f_1(\textup{TimeDiff}_{ij}) + f_2(\textup{Distance}_{ij}) + \\ && f_3(\textup{SampleDelay}_{ij}) + f_4(\textup{DefecationDay}_{ij}) + \\ && \gamma_{i}, \\ \gamma_i &\sim& \mathcal{N}(0, \sigma_\gamma^2). \end{eqnarray} \]
Not many observations after datafusion left for robust modelling
Trade-off between spatial and temporal distance
Sample Delay seems to be significant
Modelling Outcomes don’t show much difference
Trade-off between Complexity and Explainability
How to minimize spatial and temporal distance at the same time?
How to use a bigger Part of the Data?
Effect of Hunting on Red Deer